See complete Problem 205 at:

gogeometry.com/problem/p205_right_triangle_area_exradii.htm

Right Triangle Area, Excircles, Exradii relatives to legs or catheti. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Friday, November 14, 2008

### Elearn Geometry Problem 205: Right Triangle Area, Exradii

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we know that Tan A/2= S/p(p-a)where S is the area of trABC and p is the semiperimeter but here angle A=90 so S/p(p-a)= Tan 45=1 so S=p(p-a) and we know rb=S/(p-b) , rc=S/(p-c) so rb.rc=S^2/(p-b)(p-c)=p(p-a)=S HENCE rb.rc=S

ReplyDeleteSolution of problem 205.

ReplyDeleteLet be s the semiperimeter of ABC, and r the inradius. From problem 200, r = s – a. From problem 202, rb = s – c and rc = s – b.

So we have S = sr = s(s – a) and

S.rb.rc = s(s – a)(s – b)(s – c) = S^2 (from Heron’s theorem). Hence S = rb.rc.

To Antonio:

ReplyDeleteThe link to problem 206 always leads to problem 205 instead. Could you fix it?

Thanks.

Nilton, what is the url of the web page with the link to problem 205?

DeleteThanks